{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GCGNORJKLM5MZ34CPKES75RTE5","short_pith_number":"pith:GCGNORJK","canonical_record":{"source":{"id":"1402.4759","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-19T18:31:26Z","cross_cats_sorted":[],"title_canon_sha256":"95590d2c9933de474b8cccb2596dcb73b41f6e2181dd7ea75822dd769f2cf6d8","abstract_canon_sha256":"2b3de133aebb1e718c4b4ae8e226df9ab73febf040c5d093f1f84ce390b36e82"},"schema_version":"1.0"},"canonical_sha256":"308cd7452a5b3accef827a892ff6332778e769c01347106655ee732e2dd45558","source":{"kind":"arxiv","id":"1402.4759","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4759","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4759v4","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4759","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"GCGNORJKLM5M","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GCGNORJKLM5MZ34C","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GCGNORJK","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GCGNORJKLM5MZ34CPKES75RTE5","target":"record","payload":{"canonical_record":{"source":{"id":"1402.4759","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-19T18:31:26Z","cross_cats_sorted":[],"title_canon_sha256":"95590d2c9933de474b8cccb2596dcb73b41f6e2181dd7ea75822dd769f2cf6d8","abstract_canon_sha256":"2b3de133aebb1e718c4b4ae8e226df9ab73febf040c5d093f1f84ce390b36e82"},"schema_version":"1.0"},"canonical_sha256":"308cd7452a5b3accef827a892ff6332778e769c01347106655ee732e2dd45558","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:39.954114Z","signature_b64":"/3JCqj8qV6uJFJ0Nyhwt2GBMybWk09V5wqaDfjJOY9n304TpvVAsZdQaZkSUR9omyJloeQ3Nff1DcLGnrFBTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"308cd7452a5b3accef827a892ff6332778e769c01347106655ee732e2dd45558","last_reissued_at":"2026-05-18T00:42:39.953646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:39.953646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.4759","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2oESTpDdPnd1LZZlZmSjo8DfJmXZ+IcMsqqklOe09MCJ5/A5wx1b6koqZD8XfPN6rMDmhzgxODb4HI+eS094Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:24:36.225434Z"},"content_sha256":"ed85388879ce54511acad207938428db6e3c373bfa93d78f56783d1a8e8c7775","schema_version":"1.0","event_id":"sha256:ed85388879ce54511acad207938428db6e3c373bfa93d78f56783d1a8e8c7775"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GCGNORJKLM5MZ34CPKES75RTE5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tree-lattice zeta functions and class numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonius Deitmar, Ming-Hsuan Kang","submitted_at":"2014-02-19T18:31:26Z","abstract_excerpt":"The theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and poles, in contrast to the compact case. The determinant formulas of Bass and Ihara hold true if one defines the determinant as limit of all finite principal minors. From this analysis, a prime geodesic theorem is derived, which, applied to special arithmetic groups, yields new asymptotic assertions on class numbers of orders in global fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4759","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FoDTmP2jGttVQOrz5IZRyNCIykqRsgxozLoW8Cat+dg/TyFs+6EbvoUgHocTsBsXg7svN/fCFk3wa4orNRF+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:24:36.225781Z"},"content_sha256":"962570f0d0544fe065e3c13b5febeaded26f64dd7cae29644cd2d5986b095a58","schema_version":"1.0","event_id":"sha256:962570f0d0544fe065e3c13b5febeaded26f64dd7cae29644cd2d5986b095a58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCGNORJKLM5MZ34CPKES75RTE5/bundle.json","state_url":"https://pith.science/pith/GCGNORJKLM5MZ34CPKES75RTE5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCGNORJKLM5MZ34CPKES75RTE5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T11:24:36Z","links":{"resolver":"https://pith.science/pith/GCGNORJKLM5MZ34CPKES75RTE5","bundle":"https://pith.science/pith/GCGNORJKLM5MZ34CPKES75RTE5/bundle.json","state":"https://pith.science/pith/GCGNORJKLM5MZ34CPKES75RTE5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCGNORJKLM5MZ34CPKES75RTE5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GCGNORJKLM5MZ34CPKES75RTE5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2b3de133aebb1e718c4b4ae8e226df9ab73febf040c5d093f1f84ce390b36e82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-19T18:31:26Z","title_canon_sha256":"95590d2c9933de474b8cccb2596dcb73b41f6e2181dd7ea75822dd769f2cf6d8"},"schema_version":"1.0","source":{"id":"1402.4759","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4759","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4759v4","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4759","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"GCGNORJKLM5M","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GCGNORJKLM5MZ34C","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GCGNORJK","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:962570f0d0544fe065e3c13b5febeaded26f64dd7cae29644cd2d5986b095a58","target":"graph","created_at":"2026-05-18T00:42:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and poles, in contrast to the compact case. The determinant formulas of Bass and Ihara hold true if one defines the determinant as limit of all finite principal minors. From this analysis, a prime geodesic theorem is derived, which, applied to special arithmetic groups, yields new asymptotic assertions on class numbers of orders in global fields.","authors_text":"Antonius Deitmar, Ming-Hsuan Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-19T18:31:26Z","title":"Tree-lattice zeta functions and class numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4759","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ed85388879ce54511acad207938428db6e3c373bfa93d78f56783d1a8e8c7775","target":"record","created_at":"2026-05-18T00:42:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2b3de133aebb1e718c4b4ae8e226df9ab73febf040c5d093f1f84ce390b36e82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-19T18:31:26Z","title_canon_sha256":"95590d2c9933de474b8cccb2596dcb73b41f6e2181dd7ea75822dd769f2cf6d8"},"schema_version":"1.0","source":{"id":"1402.4759","kind":"arxiv","version":4}},"canonical_sha256":"308cd7452a5b3accef827a892ff6332778e769c01347106655ee732e2dd45558","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"308cd7452a5b3accef827a892ff6332778e769c01347106655ee732e2dd45558","first_computed_at":"2026-05-18T00:42:39.953646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:39.953646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/3JCqj8qV6uJFJ0Nyhwt2GBMybWk09V5wqaDfjJOY9n304TpvVAsZdQaZkSUR9omyJloeQ3Nff1DcLGnrFBTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:39.954114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4759","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed85388879ce54511acad207938428db6e3c373bfa93d78f56783d1a8e8c7775","sha256:962570f0d0544fe065e3c13b5febeaded26f64dd7cae29644cd2d5986b095a58"],"state_sha256":"187d57620c8d1eeb1620f7903287893d00046febf5009bb31e692c3cf4a34b99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQYbDTyAtJqmWa4fChH2HqtJ+RwQpwzZ9W2vp+Um8UZDVJIVO5HJH4YxgMYxRfxy/13c04GA9xxGZxDe5uz1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:24:36.227684Z","bundle_sha256":"41320c5978b8f22bf8d625af832184b1f27237585ee6b344952c6048db20ee34"}}